Girl or Boy | Puzzles for Interview - Interview Preparation PDF Download

Introduction

The Boy or Girl problem is a probability question that mathematicians have discussed for a long time. But here is a puzzle for you to solve. Ankur is a forgetful person who has not seen his brother for ten years and wants to buy clothes for his children. He knows that his brother has two children and one of them is a boy born on Tuesday. Can you help Ankur find out the probability that his brother has two boys born on Tuesday?

Solution

The answer is not 1/2. There are four possible cases: his brother has two boys, one boy and one girl, one girl and one boy, or both are girls. There are seven equally likely possibilities for any one of the children of taking birth on Tuesday for all these four cases. Therefore, the total cases are 7×4- 1(as there is repetition of two boys two times). The possibility for having two boys with both of them taking birth on Tuesday will be 7×2- 1. Therefore, the answer would be 13/27.

Explanation

If you knew which child was a boy, you would be closer to the truth. But since the boy could be either the younger or the older child, the analysis is more subtle. The answer is not 1/2 because there are other possibilities to consider. The four possible cases are his brother having two boys, one boy and one girl, one girl and one boy, or both girls.
There are seven equally likely possibilities for any one of the children of taking birth on Tuesday for all these four cases. Therefore, the total cases are 7×4- 1(as there is repetition of two boys two times). The possibility for having two boys with both of them taking birth on Tuesday will be 7×2- 1. Therefore, the answer would be 13/27.

Conclusion

Ankur wanted to know the probability that his brother has two boys born on Tuesday. The answer is not 1/2 because there are four possible cases to consider. There are seven equally likely possibilities for any one of the children of taking birth on Tuesday for all these four cases. Therefore, the total cases are 7×4- 1(as there is repetition of two boys two times). The possibility for having two boys with both of them taking birth on Tuesday will be 7×2- 1. Therefore, the answer would be 13/27.